no. 3-4
Ordinary Differential Equations/Partial Differential Equations
Reduction method for studying localized solutions of neural field equations on the Poincaré disk
[Méthode de réduction pour lʼétude de solutions localisées dʼéquations de champs neuronaux posées sur le disque de Poincaré]

Présenté par : the Editorial Board

Faye, Grégory1
1 NeuroMathComp Laboratory, INRIA, Sophia-Antipolis, 2004, route des Lucioles, BP 93, 06902 Sophia-Antipolis, France
Comptes Rendus. Mathématique, Tome 350 (2012) no. 3-4, pp. 161-166.

Dans cette Note, nous présentons une méthode de réduction pour lʼétude de solutions localisées dʼune équation intégro-différentielle définie sur le disque de Poincaré. Ce genre dʼéquation est relié au problème de modélisation des textures par le cortex visuel. Nous dérivons tout dʼabord une équation aux dérivées partielles équivalente à lʼéquation intégro-différentielle de départ et déduisons ensuite que les solutions qui sont radialement symétriques satisfont une équation différentielle ordinaire dʼordre 4.

We present a reduction method to study localized solutions of an integrodifferential equation defined on the Poincaré disk. This equation arises in a problem of texture perception modeling in the visual cortex. We first derive a partial differential equation which is equivalent to the initial integrodifferential equation and then deduce that localized solutions which are radially symmetric satisfy a fourth order ordinary differential equation.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2012.01.022
Faye, Grégory 1

1 NeuroMathComp Laboratory, INRIA, Sophia-Antipolis, 2004, route des Lucioles, BP 93, 06902 Sophia-Antipolis, France 
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Faye, Grégory. Reduction method for studying localized solutions of neural field equations on the Poincaré disk. Comptes Rendus. Mathématique, Tome 350 (2012) no. 3-4, pp. 161-166. doi : 10.1016/j.crma.2012.01.022. http://www.numdam.org/articles/10.1016/j.crma.2012.01.022/

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